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Infiltration experiments demonstrate an explicit connection between heterogeneity and anomalous diffusion behavior
Author(s) -
Filipovitch N.,
Hill K. M.,
Longjas A.,
Voller V. R.
Publication year - 2016
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2016wr018667
Subject(s) - infiltration (hvac) , fractal dimension , fractal , exponent , porous medium , scalar (mathematics) , diffusion , anomalous diffusion , porosity , mechanics , statistical physics , materials science , mathematics , physics , geometry , geotechnical engineering , geology , mathematical analysis , thermodynamics , innovation diffusion , computer science , linguistics , philosophy , knowledge management
Transport in systems containing heterogeneity distributed over multiple length scales can exhibit anomalous diffusion behaviors, where the time exponent, determining the spreading length scale of the transported scalar, differs from the expected value of n = 1 2. Here we present experimental measurements of the infiltration of glycerin, under a fixed pressure head, into a Hele‐Shaw cell containing a 3‐D printed distribution of flow obstacles; a system that is an analog for infiltration into a porous medium. In support of previously presented direct simulation results, we experimentally demonstrate that, when the obstacles are distributed as a fractal carpet with fractal dimension H < 2, the averaged progress of infiltration exhibits a subdiffusive behavior n < 1 2. We further show that observed values of the subdiffusion time exponent appear to be quadratically related to the fractal dimension of the carpet.